Method and system of predicting electric system load based on wavelet noise reduction and EMD-ARIMA

ABSTRACT

A method and a system of predicting an electric system load based on wavelet noise reduction and empirical mode decomposition-autoregressive integrated moving average (EMD-ARIMA) are provided. The method and the system belong to a field of electric system load prediction. The method includes the following steps. Raw load data of an electric system is obtained first. Next, noise reduction processing is performed on the load data through wavelet analysis. The noise-reduced load data is further processed through an EMD method to obtain different load components. Finally, ARIMA models corresponding to the different load components are built. Further, the ARIMA models are optimized through an Akaike information criterion (AIC) and a Bayesian information criterion (BIC). The load components obtained through predicting the different ARIMA models are reconstructed to obtain a final prediction result, and accuracy of load prediction is therefore effectively improved.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the priority benefit of China application serialno. 202010777451.1, filed on Aug. 5, 2020. The entirety of theabove-mentioned patent application is hereby incorporated by referenceherein and made a part of this specification.

BACKGROUND Technical Field

The disclosure relates to a field of electric system load prediction,and in particular, relates to a method and a system of predicting anelectric system load based on wavelet noise reduction and empirical modedecomposition-autoregressive integrated moving average (EMD-ARIMA).

Description of Related Art

Prediction of a power system short-term load is the core of a smart gridintegrated intelligent energy management system. An accurate short-termload prediction model may be used to facilitate reasonable planning ofongoing grid operations under effective resource management. A random,non-stationary, and nonlinearity load curve may bring challenges to theprecise modeling of short-term load prediction.

At present, a large number of researches related to power system loadprediction are provided, including the autoregressive integrated movingaverage (ARIMA) model, the Kalman filtering prediction, the Markovforecasting, the support vector machine (SVM), the artificial neuralnetwork (ANN), the long short term memory network (LSTM), and so on.Nevertheless, these single prediction methods have their ownshortcomings. Taking ARIMA for example, acting as a classic time seriesanalysis method, in ARIMA, the connection between time series data isfully-considered, and ARIMA is also an important tool for time seriesprediction. This model is suitable for processing stationary data, butthe electric system load exhibits uncertain characteristics. Althoughthe load may be stabilized through the difference method, there is stillroom for improvement for the ARIMA model when facing considerablyfluctuating load data. The filter prediction model may be used toeffectively remove Gaussian noise and non-Gaussian noise, andexcessively less calculation amount is required, but the system model isrequired to be manually given. When the system model is inaccurate, theprediction effect may drop, so that it is difficult for such model to bewidely used. The conventional artificial intelligence algorithms may notbe used to effectively capture the time series relevance of sequencedata and thus are not ideal for time series data prediction. As animproved algorithm of RNN, LSTM is one of the current research hot spotsof deep learning. But research shows that LSTM has more advantages inlong-term load prediction. Moreover, the training time of the deeplearning method is long, the convergence speed is slow, and the modelgeneralization ability needs to be further tested.

In some researches, the advantages of different algorithms begin to befully-used and are organically combined to further improve predictionprecision. For instance, the Kalman equation of state and measurementequation are established based on the ARIMA model, and the Kalmanfiltering algorithm is finally used to establish the prediction model.Nevertheless, with lack of comparison with other methods, it isdifficult to see the advantage of prediction precision. In the empiricalmode decomposition (EMD), the original load series is decomposed into aseries of sub-series, and the kernel extreme learning machine (KELM)that optimizes the weights of the output layer through particle swarmoptimization (PSO) is used to establish a prediction model. Intervalstructure of each series is built, and favorable prediction precision isachieved. However, a considerable amount of time is needed for PSOoptimization and KELM training, and when the amount of data is small,the algorithm is prone to overfitting.

Besides, in most studies on load prediction, online monitoring data isgenerally used directly. With absence of cleaning and noise reduction ofthe data, it is difficult to ensure the reliability of the data, whichalso reduces the persuasiveness of the later prediction results. Atpresent, in a small number of studies, the load data is preprocessed,aiming to further improve the precision of later predictions. Forinstance, the use of fuzzy information granulation and support vectormachine for load prediction effectively reduces the interference ofabnormal data on the final result. First, two time series models areused to match the raw data to detect the types of outliers. Next, thenoise points and missing values that exist are repaired and processed,and then a prediction model is built based on SVM. However, theprediction method used lacks further optimization.

SUMMARY

In view of the above defects or improvement requirements of the relatedart, the disclosure provides a method and a system of predicting anelectric system load based on wavelet noise reduction and empirical modedecomposition-autoregressive integrated moving average (EMD-ARIMA)through which accuracy of load prediction is effectively improved.

To realize the above purpose, according to one aspect of the disclosure,a method of predicting an electric system load based on wavelet noisereduction and EMD-ARIMA is provided, and the method includes thefollowing steps.

(1) Electric load data of an electric system corresponding to differentmoments is obtained. When the electric load data is provided at unequalintervals, interpolation is performed on the electric load data toobtain the electric load data provided at equal intervals.

(2) Noise reduction processing is performed on the electric load datathrough wavelet analysis.

(3) The noise-reduced electric load data is further processed through anEMD method to obtain different load components.

(4) ARIMA models corresponding to the different load components arebuilt.

(5) The ARIMA model corresponding to each of the load components isoptimized through an Akaike information criterion (AIC) and a Bayesianinformation criterion (BIC).

(6) The load components obtained by predicting the optimized differentARIMA models are reconstructed to obtain a final prediction result.

Preferably, the electric load data provided at equal intervals of theelectric system is: data={₁, a₂, . . . , a_(i)} i∈[1, K], where K is Kpieces of load data corresponding to K moments, and a_(i) is a value ofan i^(th) point in the load data.

Preferably, step (2) includes the following steps.

A wavelet is selected, a decomposition level is determined, and thendecomposition calculation is performed. A threshold is selected for ahigh-frequency coefficient under each decomposition scale for softthreshold quantization. One-dimensional wavelet reconstruction isperformed based on a lowest low-frequency coefficient of waveletdecomposition and a high-frequency coefficient of each layer.

Preferably, data obtained after wavelet decomposition and noisereduction are performed is: x(t)={x₁, x₂, . . . , x_(t)} t∈[1, K], whereK is K pieces of load data corresponding to K moments, and x_(t) is avalue of a t^(th) point in the load data.

Preferably, step (3) includes the following steps.

(3.1) All maximum points and all minimum points in an original seriesx(t) are identified. An upper envelope x_(up)(t) and a lower envelopex_(low)(t) are fit and formed by adopting a cubic spline interpolationmethod, and an envelope mean m(t):

${m(t)} = \frac{{x_{up}(t)} + {x_{low}(t)}}{2}$of the upper envelope and the lower envelope is calculated.

(3.2) A difference value between the original series x(t) and theenvelop mean m(t) is calculated and marked as: h(t): h(t)=x(t)−m(t).

(3.3) Whether h(t) satisfies intrinsic mode function (IMF) constraintconditions is determined, h(t) is treated as a new input series if no isdetermined, and step (3.1) to step (3.3) are repeatedly performed untilthe IMF constraint conditions are satisfied. h(t) is treated as a firstIMF component if yes is determined, h(t) is marked as c₁ (t)=h(t), c₁(t)is separated from the original series x(t), and a residual componentr₁(t): r₁ (t)=x(t)−c₁(t) is obtained.

(3.4) The residual component r₁(t) is treated as a new original series,and step (3.1) is executed again until other IMF components and oneresidual component are obtained. A final result of EMD is represented asr(t)=x(t)−c_(i)(t), where c_(i)(t) is an i^(th) IMF component, and r(t)is a final residual component representing a trend term of the originalseries.

Preferably, the IMF constraint conditions are: (a) in an entire seriesdata segment, a number of extreme points and a number of zero-crossingpoints are required to be identical or be different from each other atmost by one, and (b) at any point, a mean of an upper envelopedetermined by a maximum value and a lower envelope determined by aminimum value is zero.

Preferably, an ARIMA(p,d,q) model is a combination of an AR(p) model andan MA(q) model. The ARIMA(p,d,q) model is represented as:

${x_{t} = {\mu + {{\sum}_{i = 1}^{p}\gamma_{i}x_{t - 1}} + \xi_{t} + {{\sum}_{i = 1}^{q}\theta_{i}\xi_{t - i}}}},$where x_(t) is a current value, μ is a constant term, p is an order,γ_(i) is an autocorrelation coefficient, ξ_(t) is an error, q is anorder, θ_(i) is a parameter eliminating random fluctuation, x_(t-i) is avalue at a moment t−i, ξ_(t-i) is an error at the moment t−i.

Preferably, step (5) includes the following steps.

A difference order d value is determined corresponding to each of theARIMA models according to a plurality of differences for each of theARIMA models, and each of the ARIMA models is converted into acorresponding autoregressive moving average (ARMA) model.

Ordering is performed on a load component corresponding to each of theARMA models through an autocorrelation function (ACF) and a partialautocorrelation function (PACF) for each of the ARMA models. A pluralitygroups of p and q values are obtained. The plurality groups of the ARMAmodels are optimized through AIC and BIC corresponding to the pluralitygroups of the ARMA models. The ARIMA model corresponding to each of theload component is obtained. If a value calculated through the twoparameters AIC and BIC decrease, meaning that the model is suitable.

According to another aspect of the disclosure, a system of predicting anelectric system load based on wavelet noise reduction and EMD-ARIMA isprovided, and the system includes a data processing module, a featuredecomposition module, an ARIMA prediction model building module, anARIMA model optimization module, a component prediction module, and aprediction module.

The data processing module is configured to obtain load data of anelectric system and performs wavelet noise reduction processing on theload data.

The feature decomposition module is configured to perform EMD on thewavelet noise-reduced load data and obtains different IMF components anda residual component of the load data.

The ARIMA prediction model building module is configured to build ARIMAmodels for the different IMF components and the residual component ofthe load data obtained through EMD.

The ARIMA model optimization module is configured to optimize the ARIMAmodels of the different IMF components and the residual component.

The component prediction module is configured to perform ARIMAprediction on the different IMF components and the residual componentobtained through optimization.

The prediction module is configured to synthesize results predicted bythe component prediction module to obtain a final load predictionresult.

According to another aspect of the disclosure, the disclosure furtherprovides a computer readable storage medium storing a computer program.The computer program performs any step of the method when being executedby a processor.

In general, the above technical solutions provided by the disclosurehave the following beneficial effects compared with the related art.

At present, raw data is seldom preprocessed in the load predictionresearch. Nevertheless, in the disclosure, noise reduction is performedon load data through the wavelet analysis, and interference generated bybad data on prediction may be reduced in this way. Further, an EMD-ARIMAprediction model is built. Stationary processing is performed on anonlinear and non-stationary load time series through EMD to obtain aplurality of components. ARIMA models are built for the differentcomponents, and the ARIMA models are optimized through AIC and BIC.Reconstruction is finally performed to obtain a load prediction result,and accuracy of load prediction is therefore effectively improved.

To make the aforementioned more comprehensible, several embodimentsaccompanied with drawings are described in detail as follows.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings are included to provide a furtherunderstanding of the disclosure, and are incorporated in and constitutea part of this specification. The drawings illustrate exemplaryembodiments of the disclosure and, together with the description, serveto explain the principles of the disclosure.

FIG. 1 is a schematic flow chart of a method of predicting an electricsystem load based on wavelet noise reduction and empirical modedecomposition-autoregressive integrated moving average (EMD-ARIMA)according to an embodiment of the disclosure.

FIG. 2 provides graphs of wavelet decomposition results based on db4according to an embodiment of the disclosure.

FIG. 3A to FIG. 3B provides graphs comparing data before and afterwavelet noise reduction according to an embodiment of the disclosure,where FIG. 3A is raw load data, and

FIG. 3B is the wavelet-denoised load data.

FIG. 4 provides graphs of EMD results of a wavelet noise reduced-loadseries according to an embodiment of the disclosure.

FIG. 5 provides a graph comparing between raw data and predictionresults when an ARIMA(2,1,2) model is built for IMF1 for predictingaccording to an embodiment of the disclosure.

FIG. 6 provides graphs comparing between the raw data and the predictionresults when EMD-ARIMA is used for prediction according to an embodimentof the disclosure.

FIG. 7 is a schematic view providing a structure of a system accordingto an embodiment of the disclosure.

DESCRIPTION OF THE EMBODIMENTS

To better illustrate the goal, technical solutions, and advantages ofthe disclosure, the following embodiments accompanied with drawings areprovided so that the disclosure are further described in detail. Itshould be understood that the specific embodiments described hereinserve to explain the disclosure merely and are not used to limit thedisclosure. In addition, the technical features involved in the variousembodiments of the disclosure described below can be combined with eachother as long as the technical features do not conflict with each other.

The disclosure provides a method and a system of predicting an electricsystem load based on wavelet noise reduction and empirical modedecomposition-autoregressive integrated moving average (EMD-ARIMA).Further, prediction of daily load data of a specific region is treatedas a specific example for description. Nevertheless, the disclosure maynot only be applied to load prediction of such region but may also beapplied to prediction fields.

Raw load data of an electric system is obtained first. Next, noisereduction processing is performed on the load data through waveletanalysis. The noise-reduced load data is further processed through anEMD method to obtain different load components. Finally, ARIMA modelscorresponding to the different load components are built. Further, theARIMA models are optimized through an Akaike information criterion (AIC)and a Bayesian information criterion (BIC). The load components obtainedthrough predicting the different ARIMA models are reconstructed toobtain a final prediction result. At present, raw data is seldompreprocessed in the load prediction research. Nevertheless, in thedisclosure, noise reduction is performed on load data through thewavelet analysis, and interference generated by bad data on predictionmay be reduced in this way. Further, an EMD-ARIMA prediction model isbuilt. Stationary processing is performed on a nonlinear andnon-stationary load time series through EMD to obtain a plurality ofcomponents. ARIMA models are built for the different components, and theARIMA models are optimized through an Akaike information criterion (AIC)and a Bayesian information criterion (BIC). Reconstruction is finallyperformed to obtain a load prediction result. A wavelet thresholddenoising method requires less calculation and exhibits high processingefficiency and thus may be used to effectively improve precision of dataprocessing, and accuracy of load prediction is therefore effectivelyimproved.

As shown in FIG. 1 , in the example of load prediction of such specificregion, a schematic flow chart of a method of predicting an electricsystem load based on wavelet noise reduction and EMD-ARIMA according toan embodiment of the disclosure is provided, and the method includes thefollowing steps.

In S1, electric load data of an electric system corresponding todifferent moments is obtained. This step may be skipped if the electricload data is provided at equal intervals. If the electric load data isprovided at unequal intervals, interpolation is performed on theelectric load data to obtain the electric load data provided at equalintervals.

In the embodiments of the disclosure, the electric load data is data ofan electric system of a specific region in 2011. The electric load datais provided at equal intervals: data={a₁, a₂, . . . , a_(i)} i∈[1, K],where K is K pieces of load data corresponding to K moments, and a_(i)is a value of an i^(th) point in the load data.

In S2, noise reduction processing is performed on the electric load datathrough wavelet analysis.

In the embodiments of the disclosure, a db4 wavelet is selected, thedecomposition level is 3, and decomposition calculation is thenperformed. A threshold for a high-frequency coefficient under eachdecomposition scale is selected for soft threshold quantization.One-dimensional wavelet reconstruction is performed based on a lowestlow-frequency coefficient of wavelet decomposition and a high-frequencycoefficient of each layer. In a specific implementation process, ahigh-pass filter and a low-pass filter may be designed to respectivelyobtain the high-frequency coefficient and the low-frequency coefficient,and a length of data is halved every time the data is decomposed.Wavelet reconstruction is an inverse process of decomposition.Upsampling is performed first, that is, one 0 is inserted between everytwo numbers, convolution is performed together with a conjugate filter,and finally, convolution results are summed up. A signal isreconstructed using the coefficients of each layer. The finalhigh-frequency coefficient and low-frequency coefficient of differentscales are finally obtained as shown in FIG. 2 .

In the embodiments of the disclosure, data obtained after waveletdecomposition and noise reduction are performed is: x(t)={x₁, x₂, . . ., x_(t)} t∈[1, K], where K is K pieces of load data corresponding to Kmoments, and x_(t) is a value of a t^(th) point in the load data. FIG. 3shows comparison of data before and after noise reduction, where (a) isthe raw load data, and (b) is the wavelet-denoised load data.

In S3, the noise-reduced electric load data is further processed throughan EMD method to obtain different load components.

In the embodiments of the disclosure, in the EMD method, it is assumedthat any complex time signal is formed by a series of simple andindependent intrinsic modal functions (IMFs). Each IMF component isrequired to satisfies the following constraint conditions: (a) in anentire series data segment, a number of extreme points and a number ofzero-crossing points are required to be identical or be different fromeach other at most by one, and (b) at any point, a mean of an upperenvelope determined by a maximum value and a lower envelope determinedby a minimum value is zero.

In the embodiments of the disclosure, specific decomposition steps of agiven load series include the following.

(1) All maximum points and all minimum points in an original series x(t)are identified, an upper envelope x_(up)(t) of the maximum points and alower envelope x_(low)(t) of the minimum points are fit and formed byadopting a cubic spline interpolation method, and an envelope mean m(t):

${m(t)} = \frac{{x_{up}(t)} + {x_{low}(t)}}{2}$of the upper envelope and the lower envelope are calculated.

(2) A difference value between the original series x(t) and the envelopmean m(t) is calculated and marked as: h(t): h(t)=x(t)−m(t).

(3) Whether h(t) satisfies the IMF constraint conditions are determined,h(t) is treated as a new input series if no is determined, and step (1)to step (2) are repeatedly performed until the IMF constraint conditionsare satisfied. h(t) is treated as a first IMF component if yes isdetermined, h(t) is marked as c₁(t)=h(t), c₁(t) is separated from theoriginal series x(t), and a residual component r₁(t): r₁(t)=x(t)−c₁ (t)is obtained.

(4) The residual component r₁(t) is treated as a new original series,and the stationary processing of step (1) to step (4) are repeated untilother IMF components and one residual component are obtained. A finalresult of EMD may be represented as r(t)=x(t)−c_(i)(t), where c_(i)(t)is an i^(th) IMF component, and r(t) is a final residual componentrepresenting a trend term of the original series.

Through the EMD method, different scales or trend components may bedecomposed from the load series level by level. A series of sub-seriescomponents with different time scales are thereby formed, and thesub-series components exhibit improved stationarity and regularitycompared to the original series, and enhanced prediction precision istherefore provided.

In the embodiments of the disclosure, EMD processing is performed on thewavelet noise-reduced load data, corresponding 7 groups of the IMFcomponents and 1 group of the residual component are separated level bylevel, and the decomposition results are shown in FIG. 4 .

It can be seen that after the EMD processing is performed, differencesin levels of the load data are reduced, and changes are stabilized.Prediction may be performed through the ARIMA models.

In S4, ARIMA models corresponding to the different load components arebuilt.

In the embodiments of the disclosure, an ARIMA(p,d,q) model is actuallya combination of an AR(p) model and an MA(q) model. The “I” inARIMA(p,d,q) means to perform difference processing on a non-stationarytime series, and a parameter d in the ARIMA(p,d,q) model may bedetermined by the difference method.

AR(p) is an autoregressive model, and such model is a relationship ofdisturbance among a response x_(t) of a variable at a moment t,responses x_(t-1), x_(t-2), . . . at moments t−1, t−2, . . . , andentering of the system at the moment t, which is not directly related toprevious disturbance. The autoregressive model is required meet thestationarity requirements. The formula of a p-order autoregressiveprocess is:

${x_{t} = {\mu + {{\sum}_{i = 1}^{p}\gamma_{i}x_{t - i}} + \xi_{t}}},$where x_(t) is a current value, μ is a constant term, p is an order,γ_(i) is an autocorrelation coefficient, and ξ_(t) is an error.

An MA(q) model is a moving average model, and such model refers to lackof a direct relationship between the response x_(t) of the variable atthe moment t and the responses at the moments t−1, t−2, . . . as well asa specific relationship with disturbance of entering of the system atthe moments t−1, t−2, . . . . The moving average method may be used toeffectively eliminate random fluctuation in prediction, and the randomfluctuation refers to the accumulation of error terms in theautoregressive model. The formula of a q-order autoregressive processis:

${x_{t} = {\mu + \xi_{t} + {{\sum}_{i = 1}^{q}\theta_{i}\xi_{t - i}}}},$where q is an order, ξ_(t) is an error, and θ_(i) is a parametereliminating random fluctuation.

ARIMA(p,d,q) is an autoregressive moving average model, and such modelis a combination of autoregression and a moving average and refers to adirect relationship between the response x_(t) of the variable at themoment t and the responses x_(t-1), x_(t-2), . . . at the moments t−1,t−2, . . . as well as a specific relationship with disturbance ofentering of the system at the moments t−1, t−2, . . . . The formula is

${x_{t} = {\mu + {{\sum}_{i = 1}^{p}\gamma_{i}x_{t - i}} + \xi_{t} + {{\sum}_{i = 1}^{q}\theta_{i}\xi_{t - i}}}},$

In S5, the ARIMA models are optimized through AIC and BIC. If a valuecalculated through the two parameters AIC and BIC decrease, meaning thatthe model is suitable.

In the embodiments of the disclosure, a corresponding difference order dvalue is determined according to a plurality of differences for each ofthe ARIMA models, and each of the ARIMA models is converted into anautoregressive moving average (ARMA) model. Ordering is performed on anobtained stationary time series through an autocorrelation function(ACF) and a partial autocorrelation function (PACF). A plurality groupsof p and q values are obtained. As such, the plurality groups of themodels are optimized through AIC and BIC corresponding to the pluralitygroups of the models. The AIC formula is: AIC=−2 ln(L)+2k, and the BICformula is: BIC=−2 ln(L)+ln(n)·k, where L is maximum likelihood underthe model, n is a number of pieces of data, and k is a number of thevariables in the model. Both AIC and BIC introduce penalty terms relatedto a number of model parameters, and the penalty term of BIC is greaterthan that of AIC. Taking into account a number of samples, when thenumber of samples is excessively large, precision of the model iseffectively prevented from being excessively high, which may lead toexcessive complexity of the model. The ARIMA models of the componentsmay all be different.

In the embodiments of the disclosure, since a large number of componentsare required to be predicted, these components may not be described oneby one, description of a component IMF1 provided instead. Based on IMF1data, after AIC and BIC values of different ARIMA models are calculated,Table 1 may be obtained. It can be seen that the ARIMA(2,1,2) model maybe selected for IMF1 for prediction (AIC and BIC shall be as less aspossible). It can be seen that conditions are satisfied after a residualtest is carried out, so it may be used for load component prediction.Similarly, the ARIMA prediction models are built for IMF2 to IMF7components and residual components, and model parameters correspondingto different components are obtained, as shown in Table 2. Results ofprediction performed by building ARIMA(2,1,2) for IMF1 are as shown inFIG. 5 .

TABLE 1 AIC and BIC of Different ARIMA Models Built based on IMF1 ModelAIC BIC ARIMA (0, 1, 0) 6770.5 6777.5 ARIMA (1, 1, 1) 6485.5 6492.6ARIMA (1, 1, 2) 6489.7 6496.8 ARIMA (1, 2, 1) 6769.8 6776.8 ARIMA (1, 2,2) 6881.4 6888.4 ARIMA (2, 1, 1) 6487.3 6494.3 ARIMA (2, 1, 2) 6479.66486.6 ARIMA (2, 2, 1) 6590.0 6597.1 ARIMA (2, 2, 2) 6604.2 6611.3

TABLE 2 Model Selection for Different Components Component ARIMA (p, d,q) IMF1 ARIMA (2, 1, 2) IMF2 ARIMA (2, 1, 2) IMF3 ARIMA (2, 1, 2) IMF4ARIMA (2, 2, 2) IMF5 ARIMA (2, 1, 1) IMF6 ARIMA (2, 1, 2) IMF7 ARIMA (2,1, 2) Residual Component ARIMA (2, 2, 2)

In S6, the load components obtained through predicting the differentARIMA models are reconstructed to obtain a final prediction result.

In the embodiments of the disclosure, ARIMA models as shown in Table 2are built for different components, prediction is made by each of themodels, and prediction images are not shown. Finally, EMD inversereconstruction is performed on all of the prediction results, a specificprocess may be obtained with reference to the foregoing decompositionprocess, and the finally-obtained prediction result and errors are shownin FIG. 6 . From FIG. 6 , it can be directly seen that the raw data isclose to the prediction result, but such degree of closeness is requiredto be further explained through quantitative indicators.

In order to better present the prediction results, in the embodiments ofthe disclosure, two indicators are selected to evaluate a predictioneffect of the models, namely the root mean square error (RMSE):

${RMSE} = \sqrt{\frac{1}{n}{\sum\limits_{i = 1}^{n}\left( {y_{i} - {\hat{y}}_{i}} \right)^{2}}}$and the mean absolute error (MAE):

${{MAE} = {\frac{1}{n}{\sum\limits_{i = 1}^{n}{❘{y_{i} - {\hat{y}}_{i}}❘}}}},$where y_(i) represents the raw data, ŷ_(i) represents the predictionresult, and n represents an amount of data.

Since the level of the load data used in the embodiments of thedisclosure is large, the large values of RMSE and MAE do not mean that arelative error must be large.

The two indicators predicting the load through the conventional ARIMAmodels and performing prediction through EMD-ARIMA are calculated,processing results produced with or without the wavelet analysis arealso compared, and the final comparison results are shown in Table 3.

TABLE 3 Prediction Indicator Calculation Results through DifferentProcessing Methods No. Model RMSE MAE 1 ARIMA 7819.65 5106.37 2 waveletnoise 3178.82 1538.52 reduction + ARIMA 3 EMD-ARIMA 4353.77 2859.47 4wavelet noise 2198.64 1360.42 reduction + EMD-ARIMA

From Table 3, it can be seen that whether it is wavelet noise reductionor prediction parallel with EMD-ARIMA, the final result is significantlyaffected, and the final prediction effect is effectively improved.Compared to a conventional ARIMA model, the RMSE and MAE in the providedmethod are reduced by 71.88% and 73.36% respectively, it thus can beseen that prediction errors are significantly reduced.

FIG. 7 is a schematic view providing a structure of a system ofpredicting an electric system load based on wavelet noise reduction andEMD-ARIMA, and the system includes a data processing module 201, afeature decomposition module 202, an ARIMA prediction model buildingmodule 203, an ARIMA model optimization module 204, a componentprediction module 205, and a prediction module 206.

The data processing module 201 is configured to obtain load data of anelectric system and performs wavelet noise reduction processing on theload data.

The feature decomposition module 202 is configured to perform EMD on thewavelet noise-reduced load data and obtains different IMF components anda residual component of the load data.

The ARIMA prediction model building module 203 is configured to buildARIMA models for the different IMF components and the residual componentof the load data obtained through EMD.

The ARIMA model optimization module 204 is configured to optimize theARIMA models of the different IMF components and the residual component.

The component prediction module 205 is configured to perform ARIMAprediction on the different IMF components and the residual component.

The prediction module 206 is configured to synthesize results predictedby the component prediction module 205 to obtain a final load predictionresult.

Herein, specific implementation of each of the modules may be found withreference to the description of the method embodiments, and descriptionthereof is not repeated in the embodiments of the disclosure.

In another embodiment of the disclosure, a computer readable storagemedium storing a program instruction is also provided. The programinstruction implements the method of predicting the electric system loadbased on wavelet noise reduction and EMD-ARIMA when being executed by aprocessor according to the method embodiments.

According to the above, the method provided by the disclosure may beaccomplished in hardware and firmware, may be implemented as software ora computer code that may be stored in a recording medium (e.g., CD-ROM,RAM, floppy disk, hard disk, or magneto-optical disk), or may beaccomplished through a computer code originally stored in a remoterecording medium or a non-transitory machine-readable medium throughnetwork downloading and to be stored in a local recording medium. Inthis way, the method described herein may be processed by softwarestored on a recording medium using a general-purpose computer, adedicated processor, or programmable or dedicated hardware (e.g., ASICor FPGA). It may be understood that a computer, a processor, amicroprocessor controller, or programmable hardware includes a storagecomponent (e.g., RAM, ROM, flash memory, etc.) that may store or receivesoftware or a computer code. When the software or computer code isaccessed and executed by a computer, a processor, or hardware, theprocessing method described herein is realized. In addition, when ageneral-purpose computer accesses the code for implementing theprocessing shown herein, execution of the code converts thegeneral-purpose computer into a dedicated computer for executing theprocessing shown herein.

Note that according to implementation requirements, each step/partdescribed in the disclosure may be further divided into moresteps/parts, or two or more steps/parts or partial operations of astep/part may be combined into a new step/part to accomplish the goal ofthe disclosure.

It will be apparent to those skilled in the art that variousmodifications and variations can be made to the disclosed embodimentswithout departing from the scope or spirit of the disclosure. In view ofthe foregoing, it is intended that the disclosure covers modificationsand variations provided that they fall within the scope of the followingclaims and their equivalents.

What is claimed is:
 1. A method of predicting an electric system loadbased on wavelet noise reduction and empirical modedecomposition-autoregressive integrated moving average (EMD-ARIMA),adapted to a computer comprising a memory and a processor, wherein thememory storing a program instruction and the processor executing theprogram instruction to implement the method, wherein the methodcomprising: (1) obtaining electric load data of an electric systemcorresponding to different moments, wherein interpolation is performedon the electric load data to obtain the electric load data provided atequal intervals in response to the electric load data is provided atunequal intervals, wherein the electric load data provided at the equalintervals of the electric system is: data={a₁, a₂, . . . , a_(i)} i∈[1,K], wherein K is K pieces of the electric load data corresponding to Kmoments, and a_(i) is a value of an i^(th) point in the electric loaddata; (2) performing a wavelet noise reduction process on the electricload data through wavelet analysis, wherein data obtained after thewavelet noise reduction are performed is: x(t)={x₁, x₂, . . . , x_(t)}t∈[1, K], wherein K is K pieces of the electric load data correspondingto K moments, and x_(t) is a value of a t^(th) point in the electricload data; (3) further processing the noise-reduced electric load datathrough an EMD method to obtain different load components, wherein step(3) further comprises: (3.1) identifying all maximum points and allminimum points in an original series x(t), fitting and forming an upperenvelope x_(up)(t) and a lower envelope x_(low)(t) by adopting a cubicspline interpolation method, calculating an envelope mean m(t):${m(t)} = \frac{{x_{up}(t)} + {x_{low}(t)}}{2}$  of the upper envelopeand the lower envelope; (3.2) calculating and marking a difference valuebetween the original series x(t) and the envelop mean m(t) as: h(t):h(t)=x(t)−m(t); (3.3) determining whether h(t) satisfies intrinsic modefunction (IMF) constraint conditions, treating h(t) as a new inputseries if no is determined, repeatedly performing step (3.1) to step(3.3) until the IMF constraint conditions are satisfied, treating h(t)as a first IMF component if yes is determined, marking h(t) asc₁(t)=h(t), separating c₁(t) from the original series x(t), obtaining aresidual component r₁(t): r₁(t)=x(t)−c₁(t); and (3.4) treating theresidual component r₁(t) as a new original series, executing step (3.1)again until other IMF components and one residual component areobtained, wherein a final result of EMD is represented asr(t)=x(t)−c_(i)(t) wherein c_(i)(t) is an i^(th) IMF component, r(t) isa final residual component representing a trend term of the originalseries; (4) building ARIMA models corresponding to the different loadcomponents; (5) optimizing each of the ARIMA models through an Akaikeinformation criterion (AIC) and a Bayesian information criterion (BIC),wherein the each of the ARIMA models is corresponding to each of thedifferent load components; and (6) reconstructing the different loadcomponents obtained by predicting the optimized ARIMA models to obtain afinal prediction result.
 2. The method according to claim 1, whereinstep (2) further comprises: selecting a wavelet, determining adecomposition level, performing decomposition calculation, selecting athreshold for a high-frequency coefficient under each decompositionscale for soft threshold quantization, and performing one-dimensionalwavelet reconstruction based on a lowest low-frequency coefficient ofwavelet decomposition and a high-frequency coefficient of each layer. 3.A non-transitory computer readable storage medium, storing a programinstruction for causing a computer processor to perform, wherein theprogram instruction implements the method of predicting the electricsystem load based on wavelet noise reduction and EMD-ARIMA when beingexecuted by a processor according to claim
 2. 4. The method according toclaim 1, wherein the IMF constraint conditions are: (a) in an entireseries data segment, a number of extreme points and a number ofzero-crossing points are required to be identical or be different fromeach other at most by one, and (b) at any point, the envelop mean of theupper envelope determined by a maximum value and the lower envelopedetermined by a minimum value is zero.
 5. A non-transitory computerreadable storage medium, storing a program instruction for causing acomputer processor to perform, wherein the program instructionimplements the method of predicting the electric system load based onwavelet noise reduction and EMD-ARIMA when being executed by a processoraccording to claim
 4. 6. The method according to claim 1, wherein anARIMA(p,d,q) model is a combination of an AR(p) model and an MA(q)model, and the ARIMA(p,d,q) model is represented as:${x_{t} = {\mu + {{\sum}_{i = 1}^{p}\gamma_{i}x_{t - i}} + \xi_{i} + {{\sum}_{i = 1}^{q}\theta_{i}\xi_{t - i}}}},$where x_(t) is a current value, μ is a constant term, p is an order,γ_(i) is an autocorrelation coefficient, ξ_(t) is an error, q is anorder, θ_(i) is a parameter eliminating random fluctuation, x_(t-i) is avalue at a moment t−i, ξ_(t-i) is an error at the moment t−i.
 7. Themethod according to claim 6, wherein step (5) further comprises:determining a difference order d value corresponding to each of theARIMA models according to a plurality of differences for each of theARIMA models, converting each of the ARIMA models into a correspondingautoregressive moving average (ARMA) model; and performing ordering on aload component corresponding to each of the ARMA models through anautocorrelation function (ACF) and a partial autocorrelation function(PACF) for each of the ARMA models, obtaining a plurality groups of pand q values, optimizing the plurality groups of the ARMA models throughAIC and BIC corresponding to the plurality groups of the ARMA models,obtaining the ARIMA model corresponding to each of the load component,wherein if a value calculated through the two parameters AIC and BICdecrease, meaning that the model is suitable.
 8. A non-transitorycomputer readable storage medium, storing a program instruction forcausing a computer processor to perform, wherein the program instructionimplements the method of predicting the electric system load based onwavelet noise reduction and EMD-ARIMA when being executed by a processoraccording to claim
 7. 9. A non-transitory computer readable storagemedium, storing a program instruction for causing a computer processorto perform, wherein the program instruction implements the method ofpredicting the electric system load based on wavelet noise reduction andEMD-ARIMA when being executed by a processor according to claim
 6. 10. Anon-transitory computer readable storage medium, storing a programinstruction for causing a computer processor to perform, wherein theprogram instruction implements the method of predicting the electricsystem load based on wavelet noise reduction and EMD-ARIMA when beingexecuted by a processor according to claim
 1. 11. A system of predictingan electric system load based on wavelet noise reduction and empiricalmode decomposition-autoregressive integrated moving average (EMD-ARIMA),comprising: a memory, configured to store a program instruction; and aprocessor, coupled to the memory and configured to execute the programinstruction to: obtain electric load data of an electric systemcorresponding to different moments, wherein interpolation is performedon the electric load data to obtain the electric load data provided atequal intervals in response to the electric load data is provided atunequal intervals, wherein the electric load data provided at the equalintervals of the electric system is: data={a₁, a₂, . . . , a_(i)} i∈[1,K], wherein K is K pieces of the electric load data corresponding to Kmoments, and a_(i) is a value of an i^(th) point in the electric loaddata; perform a wavelet noise reduction process on the electric loaddata through wavelet analysis, wherein data obtained after the waveletnoise reduction are performed is: x(t)={x₁, x₂, . . . x_(t)} t∈[1, K],wherein K is K pieces of the electric load data corresponding to Kmoments, and x_(t) is a value of a t^(th) point in the electric loaddata; identify all maximum points and all minimum points in an originalseries x(t), fitting and forming an upper envelope x_(up)(t) and a lowerenvelope x_(low)(t) by adopting a cubic spline interpolation method,calculating an envelope mean m(t):${m(t)} = \frac{{x_{up}(t)} + {x_{low}(t)}}{2}$  of the upper envelopeand the lower envelope; calculate and mark a difference value betweenthe original series x(t) and the envelop mean m(t) as: h(t):h(t)=x(t)−m(t); determine whether h(t) satisfies intrinsic mode function(IMF) constraint conditions, treat h(t) as a new input series if no isdetermined; treating h(t) as a first IMF component if yes is determined,marking h(t) as c₁(t)=h(t), separating c₁(t) from the original seriesx(t), obtaining a residual component r₁(t): r₁(t)=x(t)−c₁(t) in responseto the IMF constraint conditions are satisfied; treat the residualcomponent r₁(t) as a new original series to obtain other IMF componentsand one residual component, wherein a final result of EMD is representedas r(t)=x(t)−c_(i)(t), wherein c_(i)(t) is an i^(th) IMF component, r(t)is a final residual component representing a trend term of the originalseries; build ARIMA models for the different IMF components and theresidual component of the load data obtained through EMD; optimize eachof the ARIMA models of the different IMF components and the residualcomponent; perform ARIMA prediction on the different IMF components andthe residual component obtained through optimization; and synthesizeresults predicted to obtain a final load prediction result.